Theorem o Let fbe a function that is defined on the finite closed interval [a,b] O Iffx)has finitely many discontinuities in [a,b] but bounded on [a,b],then f is integrable on [a,b] OIf f is not bounded on [a,b],then fx)is not integrable on [a,b] Theorem ⚫Let f be a function that is defined on the finite closed interval [a,b]  If f(x) has finitely many discontinuities in [a,b] but bounded on [a,b], then f is integrable on [a,b] If f is not bounded on [a,b], then f(x) is not integrable on [a,b]